### Abstract

An algorithm is developed to model the three-dimensional velocity distribution function of a sample of stars using only measurements of each star's two-dimensional tangential velocity. The algorithm works with "missing data": it reconstructs the three-dimensional distribution from data (velocity measurements) that all have one dimension that is unmeasured (the radial direction). It also accounts for covariant measurement uncertainties on the tangential velocity components. The algorithm is applied to tangential velocities measured in a kinematically unbiased sample of 11,865 stars taken from the Hipparcos catalog, chosen to lie on the main sequence and have well-measured parallaxes. The local stellar velocity distribution function of each of a set of 20 color-selected subsamples is modeled as a mixture of two three-dimensional Gaussian ellipsoids of arbitrary relative responsibility. In the fitting, one Gaussian (the "halo") is fixed at the known mean velocity and velocity variance tensor of the Galaxy halo, and the other (the "disk") is allowed to take an arbitrary mean and an arbitrary variance tensor. The mean and variance tensors (commonly known as the "velocity ellipsoid") of the disk velocity distribution are both found to be strong functions of stellar color, with long-lived populations showing larger velocity dispersion, slower mean rotation velocity, and smaller vertex deviation than short-lived populations. The local standard of rest (LSR) is inferred in the usual way, and the Sun's motion relative to the LSR is found to be (U, V, W)_{⊙} = (10.1, 4.0, 6.7) ±(0.5, 0.8, 0.2)km s^{-1}. Artificial data sets are made and analyzed, with the same error properties as the Hipparcos data, to demonstrate that the analysis is unbiased. The results are shown to be insensitive to the assumption that the velocity distributions are Gaussian.

Original language | English (US) |
---|---|

Pages (from-to) | 268-275 |

Number of pages | 8 |

Journal | Astrophysical Journal |

Volume | 629 |

Issue number | 1 I |

DOIs | |

State | Published - Aug 10 2005 |

### Fingerprint

### Keywords

- Galaxy: fundamental parameters
- Galaxy: kinematics and dynamics
- Methods: statistical
- Solar neighborhood
- Stars: kinematics

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*629*(1 I), 268-275. https://doi.org/10.1086/431572

**Modeling complete distributions with incomplete observations : The velocity ellipsoid from Hipparcos data.** / Hoog, David W.; Blanton, Michael R.; Roweis, Sam T.; Johnston, Kathryn V.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 629, no. 1 I, pp. 268-275. https://doi.org/10.1086/431572

}

TY - JOUR

T1 - Modeling complete distributions with incomplete observations

T2 - The velocity ellipsoid from Hipparcos data

AU - Hoog, David W.

AU - Blanton, Michael R.

AU - Roweis, Sam T.

AU - Johnston, Kathryn V.

PY - 2005/8/10

Y1 - 2005/8/10

N2 - An algorithm is developed to model the three-dimensional velocity distribution function of a sample of stars using only measurements of each star's two-dimensional tangential velocity. The algorithm works with "missing data": it reconstructs the three-dimensional distribution from data (velocity measurements) that all have one dimension that is unmeasured (the radial direction). It also accounts for covariant measurement uncertainties on the tangential velocity components. The algorithm is applied to tangential velocities measured in a kinematically unbiased sample of 11,865 stars taken from the Hipparcos catalog, chosen to lie on the main sequence and have well-measured parallaxes. The local stellar velocity distribution function of each of a set of 20 color-selected subsamples is modeled as a mixture of two three-dimensional Gaussian ellipsoids of arbitrary relative responsibility. In the fitting, one Gaussian (the "halo") is fixed at the known mean velocity and velocity variance tensor of the Galaxy halo, and the other (the "disk") is allowed to take an arbitrary mean and an arbitrary variance tensor. The mean and variance tensors (commonly known as the "velocity ellipsoid") of the disk velocity distribution are both found to be strong functions of stellar color, with long-lived populations showing larger velocity dispersion, slower mean rotation velocity, and smaller vertex deviation than short-lived populations. The local standard of rest (LSR) is inferred in the usual way, and the Sun's motion relative to the LSR is found to be (U, V, W)⊙ = (10.1, 4.0, 6.7) ±(0.5, 0.8, 0.2)km s-1. Artificial data sets are made and analyzed, with the same error properties as the Hipparcos data, to demonstrate that the analysis is unbiased. The results are shown to be insensitive to the assumption that the velocity distributions are Gaussian.

AB - An algorithm is developed to model the three-dimensional velocity distribution function of a sample of stars using only measurements of each star's two-dimensional tangential velocity. The algorithm works with "missing data": it reconstructs the three-dimensional distribution from data (velocity measurements) that all have one dimension that is unmeasured (the radial direction). It also accounts for covariant measurement uncertainties on the tangential velocity components. The algorithm is applied to tangential velocities measured in a kinematically unbiased sample of 11,865 stars taken from the Hipparcos catalog, chosen to lie on the main sequence and have well-measured parallaxes. The local stellar velocity distribution function of each of a set of 20 color-selected subsamples is modeled as a mixture of two three-dimensional Gaussian ellipsoids of arbitrary relative responsibility. In the fitting, one Gaussian (the "halo") is fixed at the known mean velocity and velocity variance tensor of the Galaxy halo, and the other (the "disk") is allowed to take an arbitrary mean and an arbitrary variance tensor. The mean and variance tensors (commonly known as the "velocity ellipsoid") of the disk velocity distribution are both found to be strong functions of stellar color, with long-lived populations showing larger velocity dispersion, slower mean rotation velocity, and smaller vertex deviation than short-lived populations. The local standard of rest (LSR) is inferred in the usual way, and the Sun's motion relative to the LSR is found to be (U, V, W)⊙ = (10.1, 4.0, 6.7) ±(0.5, 0.8, 0.2)km s-1. Artificial data sets are made and analyzed, with the same error properties as the Hipparcos data, to demonstrate that the analysis is unbiased. The results are shown to be insensitive to the assumption that the velocity distributions are Gaussian.

KW - Galaxy: fundamental parameters

KW - Galaxy: kinematics and dynamics

KW - Methods: statistical

KW - Solar neighborhood

KW - Stars: kinematics

UR - http://www.scopus.com/inward/record.url?scp=28144438143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28144438143&partnerID=8YFLogxK

U2 - 10.1086/431572

DO - 10.1086/431572

M3 - Article

VL - 629

SP - 268

EP - 275

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 I

ER -